To solve the inequality \( 4y + 1 > 17 \), we first isolate \( y \):
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Subtract 1 from both sides: \[ 4y > 16 \]
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Divide both sides by 4: \[ y > 4 \]
Now, to express the solution in set notation, the values of \( y \) that make the inequality true can be written as: \[ { y \in \mathbb{R} ,|, y > 4 } \]
This means that the solution set includes all real numbers greater than 4.